A sequentially variant Blotto game with one-sided and incomplete information

We develop a sequentially variant Blotto game with one-sided and incomplete information to investigate strategic interactions between a defender and an attacker whose target site values are unknown. The defender first allocates defensive resources before the attacker decides a probability distribution over which site to attack between the target sites. The attacker perfectly observes the defender's resource allocation. The attacker's type is continuous, following the attacker's private values of victoriously attacking each site. We find the game's essentially unique subgame perfect equilibrium. In equilibrium, the site the attacker attacks with a higher probability is the site with a lower expected loss for the defender when the defender defends both sites. We present numerical examples to examine (1) the impacts of the informational uncertainty concerning the attacker's site values, (2) the impacts of the site values of the defender, (3) the impacts of the site values of the attacker, and (4) the impacts of the defender's defense efficiency on the equilibrium behavior.